Problem: Rewrite as a simplified fraction. ${0.6\overline{43} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 643.4343...\\ 10x &= 6.4343...\end{align*}}$ Subtracting the two equations, we have: ${990x = 637}$ ${x = \dfrac{637}{990}} $